The invention relates to an adaptive discrete-time transversal filter for forming an estimated echo signal to cancel an unwanted actual echo signal caused by an input signal.
A filter of this type is used, for example, in echo cancellers in loudspeaking telephone sets. In such telephone sets the received signal symbols reproduced by the loudspeaker of a receiving set can be received by the microphone and be re-transmitted. This may lead to unacceptable acoustic feedback ("singing"). The echo canceller in the "sending" set has now for its task to optimise the compensation for its own signal symbols forming an echo signal and received back via the microphone of the receiving set, in order to prevent these symbols reaching the loudspeaker of the sending set. The transversal filter constructs an echo cancelling signal from a linear combination of the most recently sent symbol and the N symbols sent before that symbol, where N depends on the period of time during which the symbol sent by the set itself still influences the symbol received by that set. During each send symbol interval the transversal filter receives for each of the N symbols a coefficient modification from an adaptive control circuit and the contribution of a signal to the echo signal is calculated by multiplying, for each symbol, the associated most recent coefficient by the symbol level. For a description of the adaptive coefficient control in a transversal filter the reader be referred to N.A.M. Verhoeckx et al.: "Digital Echo Cancellation for Baseband Data Transmission"; IEEE Trans. ASSP, Vol. ASSP-27, No. 6, December 1979, pp. 768-781.
In the adaptive control circuit described in the above article, the coefficients are updated during each send symbol interval by means of the "Least Mean Square" (LMS) algorithm. This algorithm is advantageous in that it is simple, requires little computing time and is easy to implement in hardware. However, from "Adaptive Signal Processing", by B. Widrow and S. D. Stearns, Prentice Hall; Englewood Cliffs, N. J., 1985, the convergence properties of the LMS algorithm are known to degrade strongly when the input signal, thus the send signal, is strongly autocorrelated. An example of a strongly autocorrelated input signal is a speech signal, so that the echo cancellation by means of the LMS algorithm meets with problems specifically with the signals transmitted between loudspeaking telephone sets.
In the article entitled "An Adaptive Filtering Algorithm Using an Orthogonal Projection to an Affine Subspace and its Properties", by K. Ozeki and T. Umeda in: Electronics and Communications in Japan, Vol. 67A, No. 5, 1984, pp. 19-27, an adaptive algorithm is described which has good convergence properties also for autocorrelated input signals. As will be further explained hereinbelow, however, the disadvantage of this algorithm is the fact that the number of computations required for each new value of the coefficients is more than twice as large as with the LMS algorithm, which considerably augments the necessary amount of hardware and the necessary computing time.
For example, from "Linear Prediction of Speech" by J. D. Markel and A. H. Gray Jr.; Springer Verlag, 1976, it is known that the unvoiced part x[k] of a speech signal can be approached by an autoregressive model of the order of p (AR(p)) given by: ##EQU1## where n[k] is a random signal in which on average the various elements of n[k] do not show any mutual correlation.